The $({\beta }^{+}{\beta }^{+}){}_{0\nu }$ and $(\varepsilon {\beta }^{+}){}_{0\nu }$ modes of ${}^{96}\mathrm{Ru}$, ${}^{102}\mathrm{Pd}$, ${}^{106}\mathrm{Cd}$, ${}^{124}\mathrm{Xe}$, ${}^{130}\mathrm{Ba}$, and ${}^{156}\mathrm{Dy}$ isotopes are studied in the projected Hartree-Fock-Bogoliubov framework for the $0^{+}\to 0^{+}$ transition. The reliability of the intrinsic wave functions required to study these decay modes has been established in our earlier works by obtaining an overall agreement between the theoretically calculated spectroscopic properties, namely yrast spectra, reduced $B(E2:0^{+}\to 2^{+})$ transition probabilities, quadrupole moments $Q(2^{+})$ and gyromagnetic factors $g(2^{+})$, and the available experimental data in the parent and daughter even-even nuclei. In the present work, the required nuclear transition matrix elements are calculated in the Majorana neutrino mass mechanism using the same set of intrinsic wave functions as used to study the two neutrino positron double-$\beta$ decay modes. Limits on effective light neutrino mass $\langle m_{\nu }\rangle$ and effective heavy neutrino mass $\langle M_N\rangle$ are extracted from the observed limits on half-lives $T_{1/2}^{0\nu }(0^{+}\to 0^{+})$ of $({\beta }^{+}{\beta }^{+}){}_{0\nu }$ and $(\varepsilon {\beta }^{+}){}_{0\nu }$ modes. We also investigate the effect of quadrupolar correlations vis-a-vis deformation on nuclear transition matrix elements (NTMEs) required to study the $({\beta }^{+}{\beta }^{+}){}_{0\nu }$ and $(\varepsilon {\beta }^{+}){}_{0\nu }$ modes.

• Received 24 June 2009

DOI:https://doi.org/10.1103/PhysRevC.80.044303